CN114814750A - Radar calibration and verification method and device, computer equipment and storage medium - Google Patents

Radar calibration and verification method and device, computer equipment and storage medium Download PDF

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CN114814750A
CN114814750A CN202210371627.2A CN202210371627A CN114814750A CN 114814750 A CN114814750 A CN 114814750A CN 202210371627 A CN202210371627 A CN 202210371627A CN 114814750 A CN114814750 A CN 114814750A
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radar
point cloud
cloud data
calibrated
coordinate system
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丁航
杨秉川
李陆洋
方牧
鲁豫杰
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Visionnav Robotics Shenzhen Co Ltd
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Visionnav Robotics Shenzhen Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40Means for monitoring or calibrating
    • G01S7/4052Means for monitoring or calibrating by simulation of echoes
    • G01S7/4082Means for monitoring or calibrating by simulation of echoes using externally generated reference signals, e.g. via remote reflector or transponder

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  • Computer Networks & Wireless Communication (AREA)
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  • Radar, Positioning & Navigation (AREA)
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Abstract

The application relates to a radar calibration method, a radar calibration device, a computer device, a storage medium and a computer program product. The method comprises the following steps: acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector; and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin. The method can realize the simultaneous calibration of a plurality of radars to be calibrated, thereby greatly improving the calibration efficiency.

Description

Radar calibration and verification method and device, computer equipment and storage medium
Technical Field
The present application relates to the field of laser radar technology, and in particular, to a radar calibration and verification method, apparatus, computer device, storage medium, and computer program product.
Background
The laser radar detects position and velocity information of a target by emitting a laser beam toward the target and receiving a beam reflected from the target. The laser radar can provide real and reliable target information for unmanned driving. In order to enhance the perception capability and the perception range of the automatic driving vehicle to the surrounding environment, a single vehicle is generally provided with a plurality of laser radars, and a large field of view can be realized by simultaneously using a plurality of radars for field-of-view splicing. Meanwhile, the robustness of the whole system can be improved by the aid of multiple radars. Due to different installation positions, coordinate systems of multiple radars are not unified, point clouds output by the multiple radars cannot be unified to the same coordinate system, and therefore external reference calibration of the multiple laser radars is of great importance.
In the related art, external reference calibration of the laser radar can only calibrate one radar to be calibrated at one time, and calibration efficiency is low.
Disclosure of Invention
In view of the above, it is necessary to provide a radar calibration method, an apparatus, a computer device, a computer readable storage medium and a computer program product, which can improve calibration efficiency.
In a first aspect, the present application provides a radar calibration method. The method comprises the following steps:
acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
In one embodiment, after establishing a reference coordinate system with an initial position of the reference radar as an origin, the method further includes:
acquiring an initial coordinate of the radar to be calibrated under the reference coordinate system;
taking the initial coordinate of the radar to be calibrated as an initialization matrix parameter of the matching algorithm;
the matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system comprises the following steps:
and matching the first point cloud data and the second point cloud data by adopting a matching algorithm with the initialized matrix parameters to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system.
In one embodiment, the matching the first point cloud data and the second point cloud data by using the matching algorithm with the initialized matrix parameter to obtain an external reference matrix of the radar to be calibrated in a reference coordinate system includes:
generating map data to be matched according to the first point cloud data;
obtaining a standard normal distribution parameter of the first point cloud data according to the map data to be matched;
obtaining a standard normal distribution parameter of the second point cloud data according to the second point cloud data and the initialization matrix parameter;
and obtaining an external reference matrix of the radar to be calibrated under the reference coordinate system according to the standard normal distribution parameters of the first point cloud data and the standard normal distribution parameters of the second point cloud data.
In one embodiment, the matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated in a reference coordinate system includes:
acquiring first sub-point cloud data in the first point cloud data, wherein the acquisition time range of the first point cloud data is the same as that of the second point cloud data;
and matching the first sub-point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system.
In one embodiment, the reflectors include circular reflectors, triangular reflectors, and polygonal reflectors.
In a second aspect, the application further provides a radar calibration device. The device comprises:
the point cloud acquisition module is used for acquiring first point cloud data received by the reference radar in the moving process according to a preset route and second point cloud data received by the radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and the point cloud matching module is used for matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
In a third aspect, the present application also provides a computer device. The computer device comprises a memory storing a computer program and a processor implementing the following steps when executing the computer program:
acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
In a fourth aspect, the present application further provides a computer-readable storage medium. The computer-readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of:
acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
In a fifth aspect, the present application further provides a computer program product. The computer program product comprising a computer program which when executed by a processor performs the steps of:
acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
According to the radar calibration method, the radar calibration device, the computer equipment, the storage medium and the computer program product, first point cloud data received by a reference radar in the moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene are obtained; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector; and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin. According to the method and the device, the first point cloud data of the full scene received by the reference radar in the process of moving along the preset route are matched with the second point cloud data of the local scenes received by the multiple radars to be calibrated under the same scene, the external parameter matrixes of the radars to be calibrated are obtained respectively, the calibration work of the multiple radars to be calibrated can be completed simultaneously, and the calibration efficiency is greatly improved. Meanwhile, the reflectors in different shapes are arranged in the visible range of the radar to be calibrated, so that the intensity of the received point cloud data is stronger, and the calibration result is more accurate.
In a sixth aspect, the application further provides a radar calibration verification method. The method comprises the following steps:
acquiring third point cloud data received by a radar to be verified by scanning a preset reference plane;
converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external parameter matrix is obtained according to the radar calibration method;
and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data.
In a seventh aspect, the present application further provides a verification apparatus for radar calibration. The device comprises:
the first verification module is used for acquiring third point cloud data received by the radar to be verified when the radar to be verified scans the preset reference plane;
the second verification module is used for converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method;
and the third verification module is used for determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data.
In an eighth aspect, the present application further provides a computer device. The computer device comprises a memory storing a computer program and a processor implementing the following steps when executing the computer program:
acquiring third point cloud data received by a radar to be verified by scanning a preset reference plane;
converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method;
and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data.
In a ninth aspect, the present application further provides a computer-readable storage medium. The computer-readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of:
acquiring third point cloud data received by a radar to be verified by scanning a preset reference plane;
converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method;
and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data.
In a tenth aspect, the present application further provides a computer program product. The computer program product comprising a computer program which when executed by a processor performs the steps of:
acquiring third point cloud data received by a radar to be verified by scanning a preset reference plane;
converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method;
and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data.
According to the radar calibration verification method, the radar calibration verification device, the computer equipment, the storage medium and the computer program product, third point cloud data received by the radar to be verified by scanning the preset reference plane are obtained; converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method; and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data. According to the method, the third point cloud data received by each radar to be verified is converted into the same coordinate system through the external reference matrix of the radar to be verified obtained according to the radar calibration method, and the consistency between the radars to be verified is judged according to the flatness of the point cloud data in the same coordinate system, so that whether the radar calibration result is accurate or not is verified, and accurate verification of the radar to be verified can be achieved.
Drawings
FIG. 1 is a diagram of an exemplary radar calibration method;
FIG. 2 is a schematic flow chart diagram of a radar calibration method in one embodiment;
FIG. 3 is a schematic flow chart illustrating obtaining an external reference matrix of a radar to be calibrated in a reference coordinate system according to an embodiment;
FIG. 4 is a schematic flow chart of step 204 in one embodiment;
FIG. 5 is a schematic flow chart diagram illustrating a method for verifying radar calibration in one embodiment;
FIG. 6 is a schematic flow chart diagram illustrating a method for radar calibration and verification according to an embodiment;
FIG. 7 is a block diagram showing the structure of a radar calibration apparatus according to an embodiment;
FIG. 8 is a diagram illustrating an internal structure of a computer device according to an embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The radar calibration method provided by the embodiment of the application can be applied to the application environment shown in fig. 1. The reference radar 104 is mounted or placed on the unmanned forklift 102, the unmanned forklift 102 can move along a preset route 108, the preset route 108 passes through an area where the radar 106 to be calibrated is located and a visible range area of the radar 106 to be calibrated, and reflectors (not shown in the figure) with different shapes are mounted in the visible range area of the radar 106 to be calibrated. The unmanned forklift 102 can also be replaced by other automatic driving vehicles, and the practical application scene can be a large-scale scene such as a factory or an industrial park.
The method comprises the steps that computer equipment obtains first point cloud data received by a reference radar in the moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; the method comprises the following steps that at least one position exists in the process that a reference radar moves to an area where a radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector; and the computer equipment matches the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin. The computer equipment can be a terminal or a server, and the terminal can also acquire the first point cloud data and the second point cloud data and then send the first point cloud data and the second point cloud data to the server for processing.
In one embodiment, as shown in fig. 2, a radar calibration method is provided, which is described by taking the method as an example for being applied to a server, and includes the following steps:
step 202, acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; the method comprises the following steps that at least one position exists in the process that a reference radar moves to an area where a radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector.
The server obtains first point cloud data received by the reference radar in the moving process according to a preset route and second point cloud data received by the radar to be calibrated in the same scene. The same scene refers to areas with the same visual range, and may be an indoor scene or an outdoor scene, for example, a scene in the same factory or the same industrial park. In this embodiment, the number of the reference radar is only 1, the number of the radars to be calibrated is multiple, and the positions of the multiple radars to be calibrated are different from each other, i.e., the visible range areas of the radars to be calibrated are also different. In the process that the reference radar moves to the area where the radar to be calibrated is located, at least one position exists so that the visible range of the reference radar contains the visible range of the radar to be calibrated, for example, a preset route passes through the area where the radar to be calibrated is located and the visible range area of the radar to be calibrated, so that the visible range of the reference radar contains the visible range of the radar to be calibrated, the aim is to enable the reference radar to scan point cloud data scanned by the radar to be calibrated, and the method is applicable to each radar to be calibrated. Meanwhile, the reflectors with different shapes are installed in different visible ranges of the to-be-calibrated radar, for example, the circular reflector is installed in the visible range of the to-be-calibrated radar A, the triangular reflector is installed in the visible range of the to-be-calibrated radar B, the square reflector is installed in the visible range of the to-be-calibrated radar C, the pentagonal reflector is installed in the visible range of the to-be-calibrated radar D, and the like. Due to the fact that the reflectors in different shapes are installed in the visual range of the different radars to be calibrated, the radars to be calibrated can receive point cloud data reflected by the reflectors installed in the visual range, and the situation that the visual range of the reference radar contains the visual range of the radars to be calibrated exists in the moving process of the reference radar, namely the reference radar can receive the point cloud data received by the radars to be calibrated and transmitted by the reflectors installed in the visual range, namely the first point cloud data and the second point cloud data both contain the point cloud data reflected by the reflectors.
In this embodiment, different radars to be calibrated are fixedly installed at different positions, so that the visible ranges of the different radars to be calibrated may overlap or may not overlap at all. The reference radar acquires first point cloud data along a preset route, and the radar to be calibrated acquires second point cloud data in a corresponding visual range, namely the first point cloud data comprises the second point cloud data received by all the radars to be calibrated.
And 204, matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
And the server matches the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under the reference coordinate system. The matching algorithm refers to a point cloud matching algorithm, and aims to compare differences between the two and obtain a relationship between the two. Common Point cloud matching algorithms include an ICP (Iterative Closest Point) algorithm and an NDT (Normal Distribution Transform) algorithm. The reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin. For example, the initial position of the reference radar may be used as an origin, the position of the initial position of the reference radar may be selected within a range of 3-5 meters from any radar to be calibrated, and any two coordinate axes, such as an X axis and a Y axis, in the reference coordinate system are constructed on the horizontal plane of the reference radar. Meanwhile, the radar to be calibrated and the reference radar are positioned on the same horizontal plane, and the calculation complexity in the matching process can be reduced.
According to the radar calibration method, first point cloud data received by a reference radar in the moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene are obtained; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector; and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin. According to the method and the device, the first point cloud data of the full scene received by the reference radar along the process of the preset route are matched with the second point cloud data of the local scene received by the multiple radars to be calibrated in the same scene, the external parameter matrix of each radar to be calibrated is obtained respectively, the calibration work of the multiple radars to be calibrated can be completed simultaneously, and the calibration efficiency is greatly improved. Meanwhile, the reflectors in different shapes are arranged in the visible range of the radar to be calibrated, so that the intensity of the received point cloud data is stronger, and the calibration result is more accurate.
In one embodiment, after establishing the reference coordinate system with the initial position of the reference radar as the origin, the method further includes:
and acquiring an initial coordinate of the radar to be calibrated in the reference coordinate system.
After the reference coordinate system is established, the offset of each radar to be calibrated relative to the origin under the reference coordinate system can be obtained through manual measurement or equipment measurement, and then the initial coordinate of each radar to be calibrated can be obtained.
And taking the initial coordinates of the radar to be calibrated as the initialization matrix parameters of the matching algorithm.
And taking the initial coordinate of the radar to be calibrated as an initial distance value, and inputting the initial distance value into a matching algorithm to be used as an initialized external parameter matrix parameter.
Matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the external reference matrix comprises the following steps:
and matching the first point cloud data and the second point cloud data by adopting a matching algorithm with the initialized matrix parameters to obtain an external reference matrix of the radar to be calibrated under the reference coordinate system.
According to the method and the device, the obtained initial coordinates of the radar to be calibrated are used as the initial matrix parameters of the matching algorithm, so that the matching precision of the matching algorithm is improved, and meanwhile, the operation speed of the matching algorithm can be improved.
In an embodiment, as shown in fig. 3, matching the first point cloud data and the second point cloud data by using a matching algorithm with initialized matrix parameters to obtain an external reference matrix of the radar to be calibrated in the reference coordinate system, includes:
step 302, generating map data to be matched according to the first point cloud data.
The map data to be matched is generated by using a mapping tool for the first point cloud data received by the reference radar during the movement along the preset route, for example, the map data to be matched may be generated by using SLAM (simultaneous localization and mapping).
And 304, obtaining a standard normal distribution parameter of the first point cloud data according to the map data to be matched.
In this embodiment, a voxel meshing method may be used to perform downsampling on the map data to be matched to obtain first target point cloud data, and calculate a standard normal distribution of the first target point cloud data in each mesh to obtain a corresponding standard normal distribution of the first point cloud data in each mesh. The size and the number of the grids can be set according to requirements.
And step 306, obtaining a standard normal distribution parameter of the second point cloud data according to the second point cloud data and the initialization matrix parameter.
In this embodiment, the product of the second point cloud data and the initialization matrix parameter may be used as second point cloud initial data, the second point cloud initial data is down-sampled according to a voxel meshing method to obtain second point cloud target data, and the probability that each second point cloud target data falls into the grid corresponding to the first point cloud data is calculated, so as to obtain a standard normal distribution parameter corresponding to the second point cloud target data.
And 308, obtaining an external reference matrix of the radar to be calibrated under the reference coordinate system according to the standard normal distribution parameters of the first point cloud data and the standard normal distribution parameters of the second point cloud data.
Respectively performing down-sampling on the first point cloud data and the second point cloud data according to a voxel gridding method; dividing the space where the first point cloud data is located into a plurality of three-dimensional grids, and calculating a corresponding probability density function for each grid based on point cloud distribution in the grid; aiming at each second point cloud data, mapping each second point cloud data to a coordinate system where the first point cloud data is located according to the initialization matrix parameters to obtain corresponding mapping points; calculating the probability of each mapping point falling into the corresponding grid according to the normal distribution parameter of the first point cloud data of the grid, and obtaining a score value corresponding to the coordinate transformation parameter according to the probability; and continuously optimizing the score value until a preset convergence condition is met, and obtaining a coordinate transformation parameter corresponding to the optimal score value, namely an external reference matrix of the radar to be calibrated under the reference coordinate system. The preset convergence condition may be a preset iteration number, a preset fraction value, or the like. For example, the preset convergence condition may also be that when the score value reaches a certain maximum value, the iteration is stopped when the score values obtained after the iteration is continued for a preset number of times are all smaller than the maximum value, and the coordinate transformation parameter corresponding to the maximum value is used as the external reference matrix of the radar to be calibrated in the reference coordinate system.
In one specific example, the first point cloud data and the second point cloud data are matched using the NDT algorithm as follows:
(1) and respectively downsampling the first point cloud data and the second point cloud data according to a voxel gridding method. The input point cloud data is created into a three-dimensional voxel grid according to a voxel meshing method, the voxel grid can be imagined as a set of tiny space three-dimensional cubes, then in each voxel, namely the three-dimensional cube, the center of gravity of all the points in the voxel is used for approximately displaying other points in the voxel, so that all the points in the voxel are finally represented by one center of gravity point, and the filtered point cloud is obtained after all the voxels are processed. Namely, the shape characteristics of the point cloud are maintained while the data amount of the point cloud is reduced.
(2) And dividing the space where the first point cloud data is located into a plurality of three-dimensional grids, and calculating a probability density function of each grid based on point cloud distribution in the grid.
Mean value:
Figure BDA0003588929530000111
wherein,
Figure BDA0003588929530000112
representing all first point cloud data in a grid.
Covariance matrix:
Figure BDA0003588929530000113
the probability density function for a trellis is:
Figure BDA0003588929530000121
(3) aiming at each second point cloud data, mapping each second point cloud data to a coordinate system where the first point cloud data is located according to the initialization matrix parameters to obtain corresponding mapping points; calculating the probability of each mapping point falling in the corresponding grid according to the normal distribution parameters of the grids
Figure BDA0003588929530000122
And taking the sum of the probabilities of each mapping point falling in the corresponding grid as the fraction value of the coordinate transformation parameter T of the current round
Figure BDA0003588929530000123
Evaluation was performed.
Figure BDA0003588929530000124
Figure BDA0003588929530000125
Wherein,
Figure BDA0003588929530000126
represents mapping points, n represents the number of grids corresponding to the mapping points, d1 and d2 represent constants that advance from a standard normal distribution to a mixed normal distribution,
Figure BDA0003588929530000127
to map the point mean vector, ∑ k Is the mapping point covariance.
Three-dimensional transformation matrix in NDT algorithm
Figure BDA0003588929530000128
Can be expressed as:
Figure BDA0003588929530000129
in the formula,
Figure BDA00035889295300001210
t=[t x t y t z ],r=[r x r y r z ],s=sinΦ,c=cosΦ,t x ,t y ,t z respectively, the positional offsets on the x, y and z coordinate axes, r x ,r y ,r z Respectively representing the angle offset in the x, y and z directions, and phi is the included angle between the mapping point and the first point cloud.
(4) Using Newton's optimization algorithm to the above fraction values
Figure BDA00035889295300001211
Is optimized, namely is obtained
Figure BDA00035889295300001212
Is measured. The newton's algorithm, also known as the fast descent method, has the following basic formula:
HΔp=-g
g is a Jacobian matrix, and the expression is as follows:
Figure BDA00035889295300001213
Figure BDA00035889295300001214
representing the deviation of the mapped points from the mean of the mapped points.
H is a Hessian matrix, and the formula is as follows:
Figure BDA0003588929530000131
(5) and (5) continuously circulating the steps (3) to (4) until a preset convergence condition is met.
In an embodiment, as shown in fig. 4, matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated in the reference coordinate system includes:
step 402, obtaining first sub-point cloud data in the first point cloud data, wherein the collection time range of the first sub-point cloud data is the same as that of the second point cloud data.
The first point cloud data is received by the reference radar in the process of moving according to the preset route, namely the first point cloud data comprises point cloud data in a visible range on the whole preset route, so that first sub-point cloud data in the first point cloud data, which is in the same time range as the second point cloud data, can be selected according to the acquisition time range. That is, the visual range corresponding to the first sub-point cloud data is the same as the visual range corresponding to the second point cloud data, so that the matching degree of the first sub-point cloud data and the second point cloud data can be improved. And each second point cloud data received by the radar to be calibrated corresponds to one first sub-point cloud data.
And step 404, matching the first sub-point cloud data and the second sub-point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system.
The server can match the second point cloud data and the first sub-point cloud data in the corresponding acquisition time range according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated, corresponding to the second point cloud data, under the reference coordinate system.
In one embodiment, the light reflectors include circular reflectors, triangular reflectors, and polygonal reflectors.
In this embodiment, reflectors of different shapes are installed in different visible ranges of the radar to be calibrated, and the reflectors include circular reflectors, triangular reflectors, quadrilateral reflectors, pentagonal reflectors and other polygonal reflectors. The specific shape is not limited in the visual range of the same radar to be calibrated, and only different visual ranges of the radar to be calibrated correspond to the reflectors in different shapes. The size, material, etc. of the specific reflector are selected according to the actual application scenario, and are not further limited herein. The reflectors with different shapes are arranged in the visual ranges of different radars to be calibrated, so that the strength difference between the second point cloud data received by the different radars to be calibrated is increased, and the accuracy of point cloud data matching can be improved when the matching algorithm is used for matching the first point cloud data and the second point cloud data.
In one embodiment, as shown in fig. 5, a method for verifying radar calibration is provided, which is described by taking the method as an example for being applied to a server, and includes the following steps:
step 502, acquiring third point cloud data received by the radar to be verified when the radar to be verified scans the preset reference plane.
And the server acquires third point cloud data received by the radar to be verified by scanning the preset reference plane. The radar to be verified comprises a plurality of radars to be verified, and the plurality of radars to be verified are calibrated based on the same reference radar. The predetermined reference plane may be any plane, for example, a flat floor or wall. In one possible implementation manner, third point cloud data received by a plurality of radars to be verified by scanning a preset reference plane at the same time may be obtained.
Step 504, converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; and the external reference matrix is obtained according to the radar calibration method.
And obtaining an external reference matrix of the radar to be verified according to the radar calibration method, wherein the external reference matrix represents the conversion relation between the coordinate system of the radar to be calibrated and the world coordinate system. And the server can convert the third point cloud data received by all the radars to be verified into the same coordinate system according to the external parameter matrix of the radars to be verified to obtain the fourth point cloud data.
And step 506, determining whether the radar calibration result is accurate according to the flatness of the fourth point cloud data.
And converting the third point cloud data received by the to-be-verified radar needing verification into the same coordinate system to obtain fourth point cloud data corresponding to the third point cloud data received by the to-be-verified radar needing verification, and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data. The radar calibration result may be an external parameter matrix corresponding to the radar to be verified. If the flatness of the fourth point cloud data is larger than the flatness threshold value, determining that the radar calibration result is accurate; and if the flatness of the fourth point cloud data is smaller than the flatness threshold value, determining that the radar calibration result is inaccurate.
In a possible implementation manner, the flatness of the fourth point cloud data can be determined according to the range size of the coordinates of the fourth point cloud data in the same coordinate system on the same coordinate axis. For example, if the coordinate ranges of the fourth point cloud data on the X axis and the Y axis are both larger than the coordinate range on the Z axis, determining the flatness of the fourth point cloud data according to the coordinate range on the Z axis, wherein the smaller the coordinate range on the Z axis is, the better the flatness of the fourth point cloud data is; or a standard reference plane can be established, the standard reference plane is parallel to the plane where the X-axis and the Y-axis are located, or the plane where the X-axis and the Y-axis are located, the distance from each fourth point cloud data to the standard reference plane is calculated, the flatness of the fourth point cloud data is determined according to the range of the distance from each fourth point cloud data to the standard reference plane, and if the range of the distance from the fourth point cloud data to the standard reference plane is smaller, the flatness of the fourth point cloud data is better.
In another possible implementation manner, Normal distributions (Normal distributions) of fourth cloud data corresponding to each radar to be verified are respectively calculated, differences among the Normal distributions of the fourth cloud data corresponding to each radar to be verified are compared, and the flatness of the fourth cloud data is determined according to the differences among the Normal distributions. The smaller the difference between the normal distributions is, the better the flatness of the fourth point cloud data is.
According to the radar calibration verification method, third point cloud data received by the radar to be verified by scanning the preset reference plane are obtained; converting the third point cloud data received by the radars to be verified into the same coordinate system according to the external parameter matrix of the radars to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method; and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data. In this embodiment, the third point cloud data received by each radar to be verified is converted into the same coordinate system through the external reference matrix of the radar to be verified obtained according to the radar calibration method, and the consistency between the radars to be verified is judged according to the flatness of the point cloud data in the same coordinate system, so as to verify whether the radar calibration result is accurate, and accurate verification of the radar to be verified can be realized.
In one embodiment, as shown in fig. 6, there is provided a radar calibration and verification method, including the following steps:
step 602, acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; the method comprises the following steps that at least one position exists in the process that a reference radar moves to an area where a radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector.
The first point cloud data is point cloud data scanned by the reference radar in the moving process according to a preset route, the second point cloud data is point cloud data scanned by the radar to be calibrated in the same scene, and the preset route passes through an area where the radar to be calibrated is located and a visible range area of the radar to be calibrated, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated. Meanwhile, different reflectors with different shapes are installed in the visible range of the radar to be calibrated, for example, a circular reflector is installed in the visible range of the radar A to be calibrated, a triangular reflector is installed in the visible range of the radar B to be calibrated, a square reflector is installed in the visible range of the radar C to be calibrated, a pentagonal reflector is installed in the visible range of the radar D to be calibrated, and the like.
And step 604, matching the first point cloud data and the second point cloud data according to an NDT matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
The external reference matrix is used for representing the transformation relation between the coordinate system of the radar to be calibrated and the reference coordinate system. The reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin. For example, the initial position of the reference radar may be used as the origin, and the initial position of the reference radar may be selected to be within 3-5 meters of any radar to be calibrated.
Step 606, obtaining third point cloud data received by the radar to be verified when the radar scans the preset reference plane.
And the server acquires third point cloud data received by the radar to be verified by scanning the preset reference plane. The radar to be verified comprises a plurality of radars to be verified, and the plurality of radars to be verified are calibrated based on the same reference radar. In this embodiment, the radar to be calibrated in steps 602 to 604 may be used as a radar to be verified to perform accuracy verification of the calibration result.
Step 608, converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified, so as to obtain fourth point cloud data; and obtaining the external parameter matrix according to the radar calibration method.
And after the external parameter matrix of the radar to be verified is obtained according to the radar calibration method, converting the cloud data of the third point received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified, and obtaining the cloud data of the fourth point.
And step 610, determining whether the radar calibration result is accurate according to the flatness of the fourth point cloud data.
By setting a flatness threshold, if the flatness of the fourth point cloud data is greater than the flatness threshold, determining that the radar calibration result is accurate; and if the flatness of the fourth point cloud data is smaller than the flatness threshold value, determining that the radar calibration result is inaccurate.
According to the radar calibration and verification method, multiple radars to be calibrated can be calibrated simultaneously by the radar calibration method, calibration results with high precision, namely the external parameter matrixes corresponding to the radars to be calibrated, can be obtained, and then the calibration results obtained in the previous step are verified by the radar calibration verification method, so that accurate verification of the radar calibration results is realized.
It should be understood that, although the steps in the flowcharts related to the embodiments as described above are sequentially displayed as indicated by arrows, the steps are not necessarily performed sequentially as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a part of the steps in the flowcharts related to the embodiments described above may include multiple steps or multiple stages, which are not necessarily performed at the same time, but may be performed at different times, and the execution order of the steps or stages is not necessarily sequential, but may be rotated or alternated with other steps or at least a part of the steps or stages in other steps.
Based on the same inventive concept, the embodiment of the application also provides a radar calibration device for realizing the radar calibration method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the method, so the specific limitations in one or more embodiments of the radar calibration device provided below can be referred to the limitations of the radar calibration method in the foregoing, and details are not described herein again.
In one embodiment, as shown in fig. 7, there is provided a radar calibration apparatus including: a point cloud acquisition module 702 and a point cloud matching module 704, wherein:
the point cloud obtaining module 702 is configured to obtain first point cloud data received by the reference radar in a moving process according to a preset route and second point cloud data received by the radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and the point cloud matching module 704 is configured to match the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, where the reference coordinate system is a coordinate system established by using an initial position of the reference radar as an origin.
In one embodiment, the radar calibration apparatus further includes an initialization module configured to:
acquiring an initial coordinate of the radar to be calibrated under the reference coordinate system;
taking the initial coordinate of the radar to be calibrated as an initialization matrix parameter of the matching algorithm;
the point cloud matching module 704 is further configured to:
and matching the first point cloud data and the second point cloud data by adopting a matching algorithm with the initialized matrix parameters to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system.
In one embodiment, the point cloud matching module 704 is further configured to:
generating map data to be matched according to the first point cloud data;
obtaining a standard normal distribution parameter of the first point cloud data according to the map data to be matched;
obtaining a standard normal distribution parameter of the second point cloud data according to the second point cloud data and the initialization matrix parameter;
and obtaining an external reference matrix of the radar to be calibrated under the reference coordinate system according to the standard normal distribution parameters of the first point cloud data and the standard normal distribution parameters of the second point cloud data.
In one embodiment, the point cloud matching module 704 is further configured to:
acquiring first sub-point cloud data in the first point cloud data, wherein the acquisition time range of the first point cloud data is the same as that of the second point cloud data;
and matching the first sub-point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system.
Based on the same inventive concept, the embodiment of the application also provides a radar calibration verification device for realizing the radar calibration verification method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the method, so that specific limitations in one or more embodiments of the radar calibration device provided below can be referred to the limitations of the verification method for radar calibration in the foregoing, and details are not described herein again.
In one embodiment, a radar calibration verification apparatus is provided, including:
the first verification module is used for acquiring third point cloud data received by the radar to be verified when the radar to be verified scans the preset reference plane;
the second verification module is used for converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method;
and the third verification module is used for determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data.
All or part of the modules in the radar calibration device or the radar calibration verification device can be realized by software, hardware and a combination thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.
In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as shown in fig. 8. The computer device includes a processor, a memory, and a network interface connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The database of the computer device is used for storing point cloud data. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a radar calibration method or a verification method of radar calibration.
Those skilled in the art will appreciate that the architecture shown in fig. 8 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In an embodiment, a computer device is provided, which includes a memory and a processor, the memory stores a computer program, and the processor implements the steps of the radar calibration method in the above embodiment when executing the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the radar calibration method in the above-mentioned embodiments.
In an embodiment, a computer program product is provided, comprising a computer program which, when being executed by a processor, carries out the steps of the radar calibration method of the above embodiments.
In an embodiment, a computer device is provided, which includes a memory and a processor, the memory stores a computer program, and the processor implements the steps of the method for verifying radar calibration in the above embodiment when executing the computer program.
In an embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method for verifying a radar calibration according to the above-mentioned embodiments.
In an embodiment, a computer program product is provided, comprising a computer program which, when being executed by a processor, carries out the steps of the method for verification of radar calibration according to the preceding embodiment.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, database, or other medium used in the embodiments provided herein may include at least one of non-volatile and volatile memory. The nonvolatile Memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash Memory, optical Memory, high-density embedded nonvolatile Memory, resistive Random Access Memory (ReRAM), Magnetic Random Access Memory (MRAM), Ferroelectric Random Access Memory (FRAM), Phase Change Memory (PCM), graphene Memory, and the like. Volatile Memory can include Random Access Memory (RAM), external cache Memory, and the like. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM), among others. The databases referred to in various embodiments provided herein may include at least one of relational and non-relational databases. The non-relational database may include, but is not limited to, a block chain based distributed database, and the like. The processors referred to in the embodiments provided herein may be general purpose processors, central processing units, graphics processors, digital signal processors, programmable logic devices, quantum computing based data processing logic devices, etc., without limitation.
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present application. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims (10)

1. A method of radar calibration, the method comprising:
acquiring first point cloud data received by a reference radar in a moving process according to a preset route and second point cloud data received by a radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
2. The method according to claim 1, wherein after establishing a reference coordinate system with an initial position of the reference radar as an origin, the method further comprises:
acquiring an initial coordinate of the radar to be calibrated under the reference coordinate system;
taking the initial coordinate of the radar to be calibrated as an initialization matrix parameter of the matching algorithm;
the matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system comprises the following steps:
and matching the first point cloud data and the second point cloud data by adopting a matching algorithm with the initialized matrix parameters to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system.
3. The method according to claim 2, wherein the matching the first point cloud data and the second point cloud data by using the matching algorithm with the initialized matrix parameters to obtain an external reference matrix of the radar to be calibrated in a reference coordinate system comprises:
generating map data to be matched according to the first point cloud data;
obtaining a standard normal distribution parameter of the first point cloud data according to the map data to be matched;
obtaining a standard normal distribution parameter of the second point cloud data according to the second point cloud data and the initialization matrix parameter;
and obtaining an external reference matrix of the radar to be calibrated under the reference coordinate system according to the standard normal distribution parameters of the first point cloud data and the standard normal distribution parameters of the second point cloud data.
4. The method according to claim 1, wherein the matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated in a reference coordinate system comprises:
acquiring first sub-point cloud data in the first point cloud data, wherein the acquisition time range of the first point cloud data is the same as that of the second point cloud data;
and matching the first sub-point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system.
5. The method of claim 1, wherein the reflectors comprise circular reflectors, triangular reflectors, and polygonal reflectors.
6. A method of validating radar calibration, the method comprising:
acquiring third point cloud data received by a radar to be verified by scanning a preset reference plane;
converting the third point cloud data received by each radar to be verified into the same coordinate system according to the external parameter matrix of the radar to be verified to obtain fourth point cloud data; the external reference matrix is obtained according to the radar calibration method of any one of claims 1 to 5;
and determining whether the radar calibration result is accurate or not according to the flatness of the fourth point cloud data.
7. A radar calibration apparatus, the apparatus comprising:
the point cloud acquisition module is used for acquiring first point cloud data received by the reference radar in the moving process according to a preset route and second point cloud data received by the radar to be calibrated in the same scene; at least one position exists in the process that the reference radar moves to the area where the radar to be calibrated is located, so that the visible range of the reference radar comprises the visible range of the radar to be calibrated; reflectors with different shapes are arranged in the visible ranges of different radars to be calibrated; the first point cloud data and the second point cloud data both comprise point cloud data reflected by the reflector;
and the point cloud matching module is used for matching the first point cloud data and the second point cloud data according to a matching algorithm to obtain an external reference matrix of the radar to be calibrated under a reference coordinate system, wherein the reference coordinate system is a coordinate system established by taking the initial position of the reference radar as an origin.
8. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method of any of claims 1 to 6.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 6.
10. A computer program product comprising a computer program, characterized in that the computer program realizes the steps of the method of any one of claims 1 to 6 when executed by a processor.
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